Mass of Projectiles

Title: Mass of Projectiles

Problem Scenario: Different bullets have different drop rates in flight. Sometimes it is hard to judge how much they would drop during flight. If you aim at the center of a bulls-eye, a bullet could drop nothing, or it could drop a foot.

Broad Question: How does mass affect a projectile object?

Specific Question: What is the impact of mass on a projectiles time of flight and distance?

Hypothesis: The projectile with the least mass, will be in the air the longest and will travel the furthest distance. The projectile with the most mass will be in the air the least and travel the least distance.

Graph of Hypothesis:

Variables

Independent Variable: Mass of the projectile.

Dependent Variable: Time the projectile is in the air before it hits the ground. Distance the projectile travels.

Variables That Need To Be Controlled: Length of pullback on slingshot, stop/start time for each experiment.

Vocabulary List That Needs Explanation

1. Projectile- any object that moves through the air with an initial force. Ex: bullet, arrow.
2. Density- The amount of matter in a given space.
3. Mass- the amount of matter.

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General Plan

I will be testing if mass has an affect on a projectiles time and distance of flight. I will have balls with different densities to alter the mass without altering the volume, and to find out which ones have the longest flight time in the air, and the ones with the shortest time in the air. To find out if density affects "hang time," I will use racquet balls as projectiles. They will be cut in half and filled with different items to vary the mass. I will make a slingshot that shoots horizontally to avoid the upwards path of the ball instead of just the horizontal path of the ball. The vertical path can add an upwards trajectory that can affect the balls path of flight.

Potential Problems And Solutions

1. If the slingshot breaks, the experiment would be useless.
2. Timer does not stop or start at the same time every time. Take many trials and average the times together. If the timer does not stop or start, scratch that one and do it over.

Safety Or Environmental Concerns

1. Projectiles hit someone. Be in a place where no one can get hurt and nothing can be broken.

Experimental Design

What is your experimental unit?

I will measure time up to hundredths of a second. I will measure distance to the half inch, and will then convert to centimeters.

Number Of Trials:

5 times for each density for flight time and distance. I will average the times and distances out so if one is slightly off, it would not affect the overall data.

Number Of Subjects In Each trial:

There will be 5 balls of different densities.

Number of Observations:
10 per each density. 50 total. 25 times for time, and 25 for distance.

When data will be collected

February 18

Where will data be collected?:

In my house to avoid wind and uneven surfaces outside.

Resources and Budget Table

Item	Number needed	Where I will get this	Cost
Poster board	1	Staples	$5
Slingshot	1	Home	N/A
Racquet balls	10	Wal-mart	$7
Stopwatch	1	Home	N/A

Detailed Procedure

1. Gather materials. 5 balls same size, different densities, and a slingshot.
2. Make slingshot rig to make experiments, and put ball into slingshot.
3. Release sling and start timer.
4. Stop timer when ball hits the ground.
5. Record results, and repeat with different densities.
6. Shoot the balls near a tape measure to measure its distance.
7. Repeat with other densities.

Diagram

Photo List

Time Line

February 1- Gather supplies
February 2- Build rig for slingshot
February 3- Perform experiment.
February 20- Write results.
March 10- Finish Wiki.
March 22- Finish poster.
March 29- Science fair!
May 29- Science fair!

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Data Table

Ball Number	Projectile Content	Mass (grams)	Time Trial 1	Time Trial 2	Time Trial 3	Time Trial 4	Time Trial 5	Average Time (seconds)
1	Nothing	23.4	0.97	0.90	0.97	1.04	0.97	0.98
2	Cotton	25.6	0.97	1.04	0.97	0.97	0.97	0.97
3	Rice	31.3	0.83	0.90	0.97	0.97	0.97	0.93
4	Ball Bearings	70.8	0.90	0.90	0.83	0.97	0.83	0.90
5	.177 Pellets	76.5	0.97	1.11	0.76	0.83	0.9	0.91
Ball Number	Projectile Content	Mass (grams)	Distance 1	Distance 2	Distance 3	Distance 4	Distance 5	Average Distance (inches)	Conversion factor	Average distance (centimeters)
1	Nothing	23.4	123.5	127	126.5	132	128	127.4	2.54	323.60
2	Cotton	25.6	119	120.5	119	119	118.5	119.2	2.54	302.77
3	Rice	31.3	98.5	103	100.5	101	102.5	101.1	2.54	256.79
4	Ball Bearings	70.8	46	45	45.5	44	44.5	45	2.54	114.30
5	.177 Pellets	76.5	42	42	44.5	42	45	43.3	2.54	109.98

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Data Analysis

All Raw Data

The time each ball had in the air was so close together, the difference was insignificant. The distance however mattered. The ball with the least mass, the one with nothing, had the farthest distance. The one with the most mass, the one with pellets, had the shortest distance. The ones in between all followed the same rate, with the lesser masses going further than the heavier ones. The times on all the balls were 0.90 seconds to 0.98 seconds. The shortest time to hit the ground was the ball bearings, which was the second heaviest mass. The longest time to hit the ground was the one with nothing in it, with 0.98 seconds. All of the times were around the same. 0.90, and 0.97 seconds came up the most frequently. The least amount of time was 0.76 by the pellets on the third trial. The longest time was 1.11 seconds, also by the pellets.

Graphs

Photos

Results

In fact, density does not affect the time a projectile is in the air. The gravitational pull is what the projectiles are affected by, and not mass. The ball with the most mass (76.5g) and the ball with the least mass (23.5g) hit the ground at the about the same time at .90 and .98 seconds. Eight hundredths is not a huge difference, so mass does not affect the time in the air. It does affect the distance though. If the projectile has lesser mass it will go further in distance than a heavier mass.

Conclusion

It is concluded that the mass of an object does not affect the drop rate. The drop rate of any object is 9.8 meters per second squared. The times were 0.90 to 0.98 seconds. The difference was 0.08 seconds between each of the masses. This is insignificant because the times are so close to each other. If the times were one second, half a second, five seconds, one second, and two seconds, the times would matter as they are off by a lot compared to eight one hundredths of a second. Distance is affected by the mass of a projectile. The ones with the lesser masses went further than the ones with a heavier mass. If a projectile is lighter, it will go further than a projectile with a heavier mass.

Discussion

This experiment was very interesting. All of the balls hit the ground at about the same time. When I changed the mass, the time was about the same. However, I also measured distance it traveled. Each ball took about 1 second to land. In this time the ball with the least mass went 3 meters. The ball with the most mass went about 1 meter. Each ball had about a one second hang time, but they went all different distances. The heaviest ball went one meter, while the lightest ball went 3 meters. Some of the times were not exact as I did not have a high-speed camera to record the exact time from take-off, to landing. I hand timed the times with a stop watch, and was probably off by a little on each launch. Fortunately, it did not matter as the times were all similar to each other. I launched the balls off of about a twelve foot high second story hallway in my house down onto the first floor. This data is great because it proves that mass does not affect drop rate, but does affect distance.

I came up with a formula found in a physics book. It was Y - Yo = V0t + ½at². This formula calculates the time it takes an object to hit the ground. Y - Yo is the distance the object travels vertically, hence the Y for the Y axis. V0t is the initial downward velocity (V0), and the time in flight (t). ½at² is half of the acceleration due to gravity 9.8 meter per second squared (a), and time in flight (t). This formula had no variable for mass, so mass did not affect the time it took to hit the ground. The theoretical time it took to hit the ground was 0.75 seconds. My experimental time was about 0.90 seconds. The times varied because the theoretical time was in a vacuum. My experiment took place in the an environment where there is air. There was air resistance so the drag coefficient is not zero like in a vacuum. Drag coefficient is a measure of an objects resistance to the air through which it passes. A vacuum has zero air resistance as a vacuum contains no air in it.

Benefit to Community and/or Science

This can benefit science/ and or the community because knowing that a bullet is not affected by gravity can help a person shoot a bulls-eye more often. A person likes to shoot will be able to judge the drop rate of their bullets all the time, as they have all the same drop rate due to gravity. An arrow with a lesser mass can hit a bulls-eye easier if you aim straight, as it flies farther than a heavier arrow. Throwing a lighter ball is better if you want to throw it for distance.

Background Research

A projectile is an object that is moved through the air without any force applied continuously . Ex: an arrow shot out of a bow. Force is applied initially, but there is no propulsion system attached to it like a rocket. A rocket would be considered a missile It has an engine that propels it by combusting materials. It can be used as a weapon, spacecraft, or any number of things. A projectile has no way of altering its path of flight once it is in the air, other than wind.

The acceleration due to gravity (g) is 9.8 meters per second squared. That means that after one second something is traveling 9.8 meters per second, then 19.6 meters per second, 29.4 meters per second, and so on. Each time it accelerates 9.8 meters the next second. A very good example of mass not affecting drop rate is the Apollo mission of dropping a hammer and feather on the Moon where there is no air resistance. The conclusion of it was that they dropped at the same rate, proving that mass does not affect drop rate.

Density is the how much matter is in a given space. In one cubic centimeter, there could be 10 grams or 100 depending on the substance. Depleted uranium is 19 grams over one cubic centimeter. That means in a one cubic centimeter cube, it has a mass of 19 grams. Water has a density of about 1 gram to centimeters cubed. Density can determine if an object sinks or floats.

References

http://www.physicsclassroom.com/Class/vectors/U3L2a.cfm

http://thehappyscientist.com/science-experiment/gravity-theory-or-law

Abstract

My experiment was a success. It proved that mass is not a factor in drop rate. I made a slingshot and used different density balls. I launched them and timed them from the start to when they hit the ground. All of them hit the ground at around the same time. I hand timed it so there was a little human error, but I did an average of 5 trials to make human error less. This can be easily replicated if you have different density balls, and something that propels them.